4.
\begin{figure}[h]
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\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{57a51cfd-7206-4f34-9744-44255789188d-3_360_1305_1151_416}
\end{figure}
A plank \(A E\), of length 6 m and mass 10 kg , rests in a horizontal position on supports at \(B\) and \(D\), where \(A B = 1 \mathrm {~m}\) and \(D E = 2 \mathrm {~m}\). A child of mass 20 kg stands at \(C\), the mid-point of \(B D\), as shown in Fig. 2. The child is modelled as a particle and the plank as a uniform rod. The child and the plank are in equilibrium. Calculate
- the magnitude of the force exerted by the support on the plank at \(B\),
- the magnitude of the force exerted by the support on the plank at \(D\).
The child now stands at a point \(F\) on the plank. The plank is in equilibrium and on the point of tilting about \(D\).
- Calculate the distance \(D F\).
\section*{5.}
\section*{Figure 3}
\includegraphics[max width=\textwidth, alt={}]{57a51cfd-7206-4f34-9744-44255789188d-4_422_1142_382_455}
Figure 3 shows a boat \(B\) of mass 400 kg held at rest on a slipway by a rope. The boat is modelled as a particle and the slipway as a rough plane inclined at \(15 ^ { \circ }\) to the horizontal. The coefficient of friction between \(B\) and the slipway is 0.2 . The rope is modelled as a light, inextensible string, parallel to a line of greatest slope of the plane. The boat is in equilibrium and on the point of sliding down the slipway. - Calculate the tension in the rope.
(6)
The boat is 50 m from the bottom of the slipway. The rope is detached from the boat and the boat slides down the slipway. - Calculate the time taken for the boat to slide to the bottom of the slipway.
(6)